Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

On the invariant density of branching diffusions


Code(s) de Classification MSC:

Résumé: We consider the invariant measure for finite systems of branching diffusions with immigration. In case of an absolute continuous immigration measure, we use the properties of the underlying stochastic flow governing the motion of every particle in order to show smoothness of the invariant density of the particle process. In case of a singular immigration measure, the main tool is Malliavin calculus which allows to show that the density is $C^{\infty}$ in any point which is not an atom of the immigration measure.

Mots Clés: branching diffusions ; invariant measure ; stochastic flows ; Malliavin calculus

Date: 2001-09-27

Prépublication numéro: PMA-688